Abstract
In [6], Cabras, Ianus and Pitis proved that in a cosymplectic manifold there does not exist any extrinsic sphere tangent to the structure vector field xi. We consider the structure vector field xi normal to the submanifold in the sense of Papaghiuc [12] and derive that a totally umbilical CR-submanifold of a cosymplectic manifold is either (i) totally geodesic, (ii) anti-invariant or (iii) an extrinsic sphere